I think that it's important to remember that politics are often, and usually, sneaky -- which means that the characters aren't always going to know the consequences of their interactions with NPCs, at least, not right away.
Inadvertently insulting a nobleman, for example, does not have to result in the nobleman calling the characters out for a duel. The insulted noble could do many things to his new enemies, anything from dropping a quiet word into the ear of the king, that these unsavory individuals should not be trusted, to working behind the scenes, trying to frame them for a murder of another of his enemies. (Ridding himself of two sets of enemies instead of just one.)
It also helps to remember that the NPCs all have plans, as has been stated earlier in the thread, that they will be trying to accomplish. If the characters do nothing to stop those plans, even if they show no interest in finding out what is going on, the plans should continue to unfold, unnoticed, in the background. The PCs may well have to deal with the consequences later. That, in my experience, keeps the game feeling more real, instead of having things happen only when the characters are around.
I hope my ideas were helpful! I'll be interested to see how it turns out for you.